# Mathematical Relativity Seminar

### Introduction to the Theory of Shock Waves (VI)

I plan to cover the following topics: Euler equations; Burger's equation; $p$-system; symmetric hyperbolic PDEs; shock formation; Lax method of solving Riemann problems; Glimm's method for solving Cauchy problems; Entropy solutions; artificial viscosity.

### Bibliography

• Joel Smoller, Shock waves and Reaction Diffusion Equations.
• Constantine Dafermos, Hyperbolic Conservation Laws in Continuum Physics.
• Alexandre Chorin and Jerrold Marsden, A Mathematical Introduction to Fluid Mechanics.
• Lecture notes of Blake Temple.